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# If X is a 3-digit number, is it odd? (1) X is a perfect square.

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Intern
Joined: 05 Oct 2017
Posts: 20
If X is a 3-digit number, is it odd? (1) X is a perfect square.  [#permalink]

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Updated on: 23 Sep 2018, 02:24
1
00:00

Difficulty:

65% (hard)

Question Stats:

40% (01:03) correct 60% (01:07) wrong based on 45 sessions

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If X is a 3-digit number, is it odd?

(1) X is a perfect square.
(2) X is a palindrome.

Originally posted by aa008 on 22 Sep 2018, 23:36.
Last edited by Bunuel on 23 Sep 2018, 02:24, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 18 Jun 2018
Posts: 186
Re: If X is a 3-digit number, is it odd? (1) X is a perfect square.  [#permalink]

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Updated on: 23 Sep 2018, 01:40
aa008 wrote:
If X is a 3- digit number, is it odd?

1). X is a perfect square.
2). X is a palindrome.

OA: E
1). X is a perfect square.
X can be $$121,144,169...$$ and so on.
Unit digit of X can be even or odd
Statement 1 alone is not sufficient.

2). X is a palindrome.
X can be $$121,131,141,.....212,222$$ and so on.
Unit digit of X can be even or odd
Statement 2 alone is not sufficient.

Combining $$(1)$$ and $$(2)$$,X should be a perfect square and a palindrome.
X can be $$121(11^2), 484(22^2)$$ as there is no unique value of X and unit digit of X can be even or odd, Combining (1) and (2) will also be insufficient.

Originally posted by Bismarck on 23 Sep 2018, 01:28.
Last edited by Bismarck on 23 Sep 2018, 01:40, edited 1 time in total.
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Joined: 04 Jan 2015
Posts: 2063
Re: If X is a 3-digit number, is it odd? (1) X is a perfect square.  [#permalink]

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23 Sep 2018, 01:35

Solution

Given:
• X is a 3-digit number

To find:
• Whether X is odd or not.

Analysing Statement 1
As per the information given in statement 1, X is a perfect square.
• Starting from 100 to 961, we have many even and odd perfect squares

Therefore, statement 1 is not sufficient

Analysing Statement 2
As per the information given in statement 2, X is palindrome.
• In 3-digits, we have many even as well as odd numbers which are palindromes.

Therefore, statement 2 is not sufficient.

Combining Both Statements
We know, X is a 3-digit perfect square, which is also a palindrome.
Possible values of X can be
• $$11^2 = 121$$
• $$22^2 = 484$$
• $$26^2 = 676$$

As we can see, X can be both even or odd.

Hence, the correct answer is option E.
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Joined: 21 May 2016
Posts: 26
Re: If X is a 3-digit number, is it odd? (1) X is a perfect square.  [#permalink]

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29 Sep 2018, 00:08
1. X can be 121,144 etc. It can be even or odd. Hence insufficient
2. X can be 121,212 etc. It can be even or odd. Hence insufficient
Combining both statements X can be 121 or 484.
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Re: If X is a 3-digit number, is it odd? (1) X is a perfect square. &nbs [#permalink] 29 Sep 2018, 00:08
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